Super-Eddington accretion discs with 3M ̇ E and 15M ̇ E around black holes with mass 10 M⊙ are examined by two-dimensional radiation hydrodynamical calculations extending from the inner disc edge to 5 × 104rg and lasting up to ∼106 rg/c. The dominant radiation pressure force in the inner region of the disc accelerates the gas vertically to the disc plane, and jets with 0.2–0.4c are formed along the rotational axis. In the case of the lower accretion rate, the initially anisotropic high-velocity jet expands outward and becomes gradually isotropic flow in the distant region. The mass-outflow rate from the outer boundary is as large as ∼1019 –1023 g s−1, but it is variable and intermittent with time; that is, the outflow switches occa- sionally to inflow in the distant region. The luminosity also varies as ∼1040–1042 erg s−1 on a long time-scale. On the other hand, the jet in the case of the higher accretion rate maintains its initial anisotropic shape even after it goes far away. The mass-outflow rate and the luminosity attain steady values of 3 × 1019 g s−1 and 1.3 × 1040 erg s−1, respectively. In accordance with the local analysis of the slim accretion disc model, the disc is thermally unstable in the case of 3M ̇ E but stable in the case of 15M ̇ E. The super-Eddington model with 15M ̇ E promises to explain the small collimation degree of the jet and the large mass-outflow rate observed in the X-ray source SS 433

We numerically examine centrifugally supported shock waves in 2D rotating accretion flows around a stellar mass (10 M⊙) and a supermassive (106 M⊙) black holes over a wide range of input accretion rates of . The resultant 2D shocks are unstable with time and the luminosities show quasi‐periodic oscillations (QPOs) with modulations of a factor of 2–3 and with periods of a tenth of a second to several hours, depending on the black hole masses. The shock oscillation model may explain the intermediate frequency QPOs with 1–10 Hz observed in the stellar mass black hole candidates and also suggest the existence of QPOs with the period of hours in active galactic nuclei. When the accretion rate is low, the luminosity increases in proportion to the accretion rate. However, when greatly exceeds the Eddington critical rate , the luminosity is insensitive to the accretion rate and is kept constantly around ∼3LE. On the other hand, the mass‐outflow rate increases in proportion to and it amounts to about a few per cent of the input mass‐flow rate.

It is well known that the rotating inviscid accretion flows with adequate injection parameters around black holes could form shock waves close to the black holes, after the flow passes through the outer sonic point and can be virtually stopped by the centrifugal force. We examine numerically such shock waves in 1D and 2D accretion flows, taking account of cooling and heating of the gas and radiation transport. The numerical results show that the shock location shifts outward compared with that in the adiabatic solutions and that the more rarefied ambient density leads to the more outward shock location. In the 2D-flow, we find an intermediate frequency QPO behavior of the shock location as is observed in the black hole candidate GRS 1915+105.

We show that a standard Shakura–Sunyaev accretion disc around a black hole with an accretion rate lower than the critical Eddington limit does show the instability in the radiation pressure dominated zone. We obtain this result performing time‐dependent simulations of accretion discs for a set of values of α and . In particular we always find the occurrence of the collapse of the disc: the instability develops always towards a collapsed gas pressure dominated disc and not towards the expansion. This result is valid for all the initial configurations we tested. We find significant convective heat flux that increases the instability development time, but is not strong enough to inhibit the disc collapse. A physical explanation of the lack of the expansion phase is proposed considering the role of the radial heat advection. Our finding is relevant since it excludes the formation of the hot Comptonizing corona – often suggested to be present – around the central object by the mechanism of the Shakura–Sunyaev instability. We also show that, in the ranges of α and values we simulated, accretion discs are crossed by significant amplitude acoustic waves.

We show that accretion discs, both in the subcritical and supercritical accretion rate regime, may exhibit significant amplitude luminosity oscillations. The luminosity time behaviour has been obtained by performing a set of time-dependent two-dimensional smoothed particle hydrodynamics simulations of accretion discs with different values of α and accretion rate. In this study, to avoid any influence of the initial disc configuration, we produced the discs injecting matter from an outer edge far from the central object. The period of oscillations is 2-50 s for the two cases, and the variation amplitude of the disc luminosity is 10 38 -10 39 erg s −1 . An explanation of this luminosity behaviour is proposed in terms of limit cycle instability; the disc oscillates between a radiation pressure dominated configuration (with a high luminosity value) and a gas pressure dominated one (with a low luminosity value). The origin of this instability is the difference between the heat produced by viscosity and the energy emitted as radiation from the disc surface (the well-known thermal instability mechanism). We support this hypothesis showing that the limit cycle behaviour produces a sequence of collapsing and refilling states of the innermost disc region.